The weights of 4 boxes are 30, 20, 60 and 70 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes and in a combination a box can be used only once?

Options

A. 180
B. 170
C. 120
D. 150

Explanation

To solve the problem, we need to determine which total weight cannot be achieved by any combination of the boxes with weights of 30 kg, 20 kg, 60 kg, and 70 kg.

### Step-by-Step Solution:

1. **List the weights of the boxes**:
- The weights of the boxes are: 30 kg, 20 kg, 60 kg, and 70 kg.

2. **Calculate the total weight of all boxes**:
- Total weight = 30 + 20 + 60 + 70 = 180 kg.

3. **Consider combinations of the boxes**:
- We can create various combinations of these weights. We can either include or exclude each box to find the possible total weights.

4. **Calculate possible weights by excluding boxes**:
- Exclude 30 kg: 180 - 30 = 150 kg
- Exclude 20 kg: 180 - 20 = 160 kg
- Exclude 60 kg: 180 - 60 = 120 kg
- Exclude 70 kg: 180 - 70 = 110 kg

5. **Calculate weights by combining boxes**:
- 30 + 20 = 50 kg
- 30 + 60 = 90 kg
- 30 + 70 = 100 kg
- 20 + 60 = 80 kg
- 20 + 70 = 90 kg
- 60 + 70 = 130 kg
- 30 + 20 + 60 = 110 kg
- 30 + 20 + 70 = 120 kg
- 30 + 60 + 70 = 160 kg
- 20 + 60 + 70 = 150 kg
- 30 + 20 + 60 + 70 = 180 kg

6. **List all possible weights**:
- From the calculations, we can derive the following possible weights:
- 0 kg (no boxes)
- 20 kg
- 30 kg
- 50 kg
- 60 kg
- 70 kg
- 80 kg
- 90 kg
- 100 kg
- 110 kg
- 120 kg
- 130 kg
- 150 kg
- 160 kg
- 180 kg

7. **Identify the missing weight**:
- Now, we check the options given in the question. If we assume the options are 110 kg, 120 kg, 150 kg, and 170 kg, we can see that:
- 110 kg is possible (30 + 20 + 60)
- 120 kg is possible (30 + 20 + 70)
- 150 kg is possible (30 + 20 + 60)
- 170 kg is NOT possible with any combination of the boxes.

### Conclusion:
The total weight that cannot be achieved by any combination of these boxes is **170 kg**.